Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168

Let the first integer be represented by: 2k

the second integer by: 2(k+1)

and the third by: 2(k+2)

Then, 2k + 2(k+1) = 2(k+2) + 30

2k + 2k + 2 = 2k + 4 + 30

4k + 2 = 2k + 34

2k = 32

k = 16

first integer: 2k = 2(16) = 32

second integer: 2(k+1) = 2(16+1) = 2(17) = 34

third integer: 2(k+2) = 2(16+2) = 2(18) = 36

Answer: 32, 34, 36

The required expression that has a value of 15 is given as P + 3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Substitute the value of p in the expression,
= P + 3
= 12 + 3
= 15

When the value of p is put on another expression there output value is not 15.

Thus, the required expression that has a value of 15 is given as P + 3.

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The inequality representing '15 is no more than a number T divided by 5' is written as 15 <= T/5, which means T divided by 5 should be greater than or equal to 15.

The phrase '15 is no more than a number T divided by 5' can be translated into an inequality. When we interpret 'no more than', it means 'less than or equal to'. Therefore, the statement can be translated into the inequality 15 <= T/5. This expresses that when you divide the number T by 5, the result should be at least 15 or any value less than 15. The interpretation of "no more than" as "less than or equal to" clarifies the inequality's meaning, emphasizing that the resulting quotient from dividing T by 5 should not exceed 15. Thus, the inequality encapsulates the relationship between the number 15 and T when considering their division by 5.

The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.

The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.

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There are 2 glasses of full water would be needed to fill the baking pan.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.

And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.

Now,

The volume of drinking water = 4 x 2 x 2

                                              = 16 inches³

And, The volume of baking pan = 4 x 8 x 2

                                                 = 64 inches³

So, Half depth of baking pan =  64 / 2

                                             = 32 inches³

Here, The volume of drinking water = 16 inches³

Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2

Therefore, There are 2 glasses of full water would be needed to fill the baking pan.

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Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.

Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:

(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.

Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.

Final answer:

To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.

Explanation:

The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:

x = y + 1 (one number exceeds the other by 1)

x + y = 29 (the sum of the numbers is 29)

Substituting the first equation into the second gives us:

(y + 1) + y = 29

2y + 1 = 29

2y = 28

y = 14

Now that we have the value of y, we can find x:

x = y + 1

x = 14 + 1

x = 15

Therefore, the two numbers are 14 and 15.

The value for x so that f(x) = 7 is at x = -3.

Using the equation of slope-intercept form (y = mx + b), where m is the gradient and b is the constant, we can find the value of x at which f(x) is equal to 7 as follows:

By observation on the graph, when x = 1, y = 3 and when x = 2, y = 2.

3 = m + b...(1)

2 = 2m + b...(2)

we multiply equation (1) by 2 and subtract equation (2) from the result;

6 - 2 = 2m - 2m + 2b - b

4 = b

putting 4 for b in equation (1) gives;

m = -1

Thus we have the equation for f(x) as

f(x) = (-1)x + 4

For f(x) = 7;

-x + 4 = 7

x = 4 - 7

x = -3.

Therefore, for f(x) to be equal to 7, the value of x is equal to -3.

Let x denotes the number of days and y denotes the total change in gas price ( in dollars).

Given : During the past seven days the price of regular gas is decreased by $0.2 each day.

Rate of decrease =$0.2 per day

Then , Total change in gas price = Rate of decrease x Number of days

i.e.[tex]y= 0.2 \times x[/tex]

i.e. [tex]y=0.2x[/tex]         (1)

To find the total change in gas price in 7 days , we put x= 7 in (1) , we get

[tex]y=0.2(7)=1.4[/tex]    

Hence, the total change in gas price in 7 days = $1.4

Answer:

0.14

Step-by-step explanation:

Let t be the total reduction. Then ...  

t = daily change * number of days  

t = 7 * 0.02  

t = $0.14!

Answer:

23

Step-by-step explanation:

Imagine that each person is assigned one wall, and all 6 people begin painting at the same time.

Since everyone will finish painting their assigned wall after 23 minutes, it takes one person 23 minutes to paint one wall.

If we have 9 people and 9 walls, we can again assign one wall to each person.

Everyone will take 23 minutes to paint their assigned wall.

In other words, it takes 23 minutes for 9 people to paint 9 walls.

Answer: its the third option